[mmaimcal] pointing error effect on interferometric phase

[Bryan Butler]

folks,

harvey correctly "point"ed out that we should see if these numbers
make any sense given what we know about VLA pointing and phase
stability (i had been thinking about this exercise for OVRO or BIMA
as well).


for the VLA, assume that the pointing error is 7 arcsec (roughly 
right), then the delay errors in fig. 17 are:

  70-m => 0.2 picosec
  34-m => 0.05 picosec

and my scaling with antenna size breaks down (more like scaling with
diameter squared now).  at any rate, assume that the scaling with 
antenna size is OK to go from 34 to 25 meters (if the scaling is with
diameter squared, this is only a 20% or so error), then you get at 7mm:

  dtau = 0.05 * (25m / 34m) * (35mm / 7mm) ~ 0.2 picosec

which gives a path error of roughly 1/18th mm.  this is about 3 deg.
of phase at 7mm.  this is much smaller than the electronic phase term, 
which is about 20 deg at 7mm, so we would never see this small 
perturbation.



for OVRO, assume that typical pointing errors are 2 arcsec, then
the delay errors are:

  70-m => 0.08 picosec
  34-m => 0.04 picosec

then you get at 1.3mm:

  dtau ~ 0.04 * (10.4m / 34m) * (35mm / 1.3mm) ~ 0.3 picosec

which gives a path error of roughly 1/10th mm.  this is about 25 deg
of phase at 1.3mm.  it seems not unrealistic to me that this type of
phase error would go relatively unnoticed, especially given that "good"
conditions usually occur at night when the pointing might be even 
better than this.



for BIMA, assume that typical pointing errors are 4 arcsec, then
the delay errors are:

  70-m => 0.1 picosec
  34-m => 0.045 picosec

and you get at 1.3mm:

  dtau ~ 0.045 * (6m / 34m) * (35mm / 1.3mm) ~ 0.2 picosec

which gives a path error of roughly 1/16th mm.  this is about 18 deg
of phase at 1.3mm, again, maybe not unreasonable?


	-bryan